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Electromagnetic Compatibility1- Introduction & examples of EMC problems2- Sources of perturbation- different perturbations- conception of sources for measurements3 – Theoretical analysis of an EMC problem- Numerical methods- Analytical methods- exploitation of data4 – Coupling- different ways of coupling- coupling in the transmission line context5 – EMC measurements6 – Protection and Shielding
Source/ Coupling/ victim modelSource(parasitic signal)Coupling channel (transmission ofenergy by conduction or radiation)Victim(consequence of theperturbation ?)Temporary malfunction?Permanent failure?Destruction?
Source/ Coupling/ victim modelCalculation of parasitic currentsconducted on a cable
Pulse propagation along linesHypothesis : TEM lines The line has to be constituted at (at least) 2 conductorssingle-wire linetwo-wire lineRLRLRsRsVs Vg-coaxial lineRLRSVo
Pulse propagation along linesClassical line model : solution of the line theoryRsLDzLDzVsLDzCDzCDzCDzRL Decomposition of the wire as a succession of (RLCG) cells. If no losses (LC) cells are consideredI(z, t)V(z, t)LDzI(z Dz, t)CDz V(z Dz, t)Applying the Kirchhoff laws:V z Dz, t V z , t L DzI z Dz, t I z, t CDzDz I t V IDz LDz z t V z, t V z, t DzV z Dz, t CDz C z C I V 2V I V CDz C Dz 2 2 z, t C 0 z t t z t V I L 0 z t
Pulse propagation along linesSolutions of the lines equations 2V 2V 2 LC 2 0 t z 2I2 V LC 0 z 2 t 2 2 2 LC 2 z 2 t z z V z, t V t V t Considering an injectedtransient pulse: 1LC z z I z, t I t I t A lossless line acts as a delay line:VV ( z , t ) V (t z / )V (0, t )dt(z, t)
Pulse propagation along linesIf we consider a retrograde wave: at t located at z, at (t dt) located at z-dz z z z z z V t t V t t V t The retrograde behavior can be seen by equating the two terms: z z z V t t V t As a consequence: t z Remark: a retrograde wave can be seen as a direct wave if we change the time andspace origins and the positive direction of propagation;V (t) z L L z V t V t consideringWe deduce:0dtt' t L z' L z z z' V t V t '
Pulse propagation along linesRelation between voltage and current z V t z I t Rc z V t z I t Rc Rc I z, t LcRsVsRL0 L L V t R c I t L L L V t R c I t L L L V z, t V t V t V t 1 L L V t L L V t L V t 1 I z, t cRc1Rc z z V t V t
Pulse propagation along linesReflection at the load extremityAt z L L I t LI LL I t 1 L R c 1 L L RL RcRL RcRLz L L AA V (t - z/ )V (t - z/ )z Lz L The extremity acts as a mirror with an attenuation coefficientz L
Pulse propagation along linesExampleRs 0Vs 30 V s - 1Rc 50 Vtotal 30 VRL 100 10 VVtotal 0 L 1/340 VL 400 m 1,33 sz L30 V30 V10 V40 V10 V30 Vz 0z L- 10 V
Pulse propagation along linesA systematic method : construction of achronogram R c L 50 c 1 20010 6 m / s cVs (t)100 V L 1 s 12Rc60 1 R s R c 200 46 st
Pulse propagation along linesLevel of injected signal along the lineVoltage sourceRsI(o, t)vs (t)M Vs (t)-Equivalent circuit:RsVs (t)V o, t Vs t R s I o, t RcV o, t Vs t RsV o, t RcInjected signal:Vo (t)AA RcMRs RcI o, t V o, t RcV o, t RcVs t Rs Rc
Pulse propagation along linesV(o, t)2512,52L/ 122L 345676,258- 12,5- 25- 37,5 Volts9101112131415161718- 4,69
Pulse propagation along linesK00646121012 L K L s K0461012K60K K L K L sK L K L s12
Pulse propagation along lines 2L 4L h t K t K L K L s t K L2 s K L2 s2 t z 0t t'z L/2K t 3 e t en s z L
Pulse propagation along linesCoupling between lines
Coupling between lines :time domain approachCoupling local time derivation of the signal Back coupling: integration over x axis duration depends on the length of the line Magnitude remains unchangedForward coupling: Magnitude increases with the length Duration is constant
Coupling between lines :frequency domain approachZ 01AV1 ( z )Z L1Z C1BZ 02ZC 2A'B'dz section ofthe linedEAZC 2BZC 2dIA'B'ZL2
Coupling between lines :frequency domain approachdEBAEquivalent scheme of of dz section of thecoupled lineZC 21 dE ZC dI 21 dE Z C dI 2dE jL12 I1 ( z )dzdVAA ' dI jC12 V1 ( z )dzdVBB 'dIA'ZC 2B'Formulation of the direct and forward waves versus parametersdVAA ' 1j L12 Z C 2 Z C1C12 I 01 ( z )e 1z dz2dVBB ' 1j L12 Z C 2 Z C1C12 I 01 ( z )e 1z dz2Coupled voltage at the input of the line:LL00V2 ( z 0) dV2 ( z ) dVAA ' ( z )e 2 z11 e ( 1 2 ) LV2 (0) j L12 Z C1Z C 2C12 I 02 1 2
Coupling between lines :frequency domain approach11 e ( 1 2 ) LV2 (0) j L12 Z C1Z C 2C12 I 02 1 2In the case of short lines: i L 1Expression of the simplified voltage:V2 (0) 1j L12 Z C1Z C 2C12 I 0 L2 The coupled voltage appears as the derivation of the current on the firstline The coefficients of the coupled signal introduce a capacitive coupling andan inductive coupling
Coupling between lines: Vabre modelEquations of coupled lines: Construction of the equivalent circuit of the dx sectionii 1 i1C xV1 xM xC xV2iNetworkequationsL x12L x i1 i 2 V1 L x t M x t V M x i1 L x i 2 2 t t i1 c x v 1 x v 1 v 2 t t v 2 v 1 v i 2 x c x 2 t t V1 V1V2 V2i 2 i2 v 1 i i L 1 M 2 x t t v 2 i i M 1 L 2 x t t i1 v v c 1 2 x t t i 2 v v 1 c 2 x t t
Coupling between lines: Vabre model v 1 i i L 1 M 2 x t t i1 v v c 1 2 x t t v 2 i i M 1 L 2 x t t i 2 v v 1 c 2 x t t Matricial form of the equations v i L x t i v c x tIn the Laplace domain:First order coupled equations v1 x Lp I1 Mp I 2 v 2 Mp I Lp I12 x i1 c pv pv12 x i 2 pv1 c pv 2 xSecond order equations 2 V1 L c M p² V1 M c L p² V2 x 2 2 V2 M c L p² V1 L c M p² V2 x 2
Coupling between lines: Vabre modelResolution of the equations, modal domain decoupling the equations2Vc V1 V22I c I1 I 22Vd V1 V22 I d I1 I 2 2 Vc x ² L M c p² V2 2 Vd L M c 2 p² V1 x ²Solution of the equations:Vc A eVd C e px / c px d Be Deppx cy dxx pp1 vcVcI c A p e B p ezc 1Id zdxx pp C p e vd D P e Vd c 1 L M c d 1 L M c 2 zc L Mczd L Mc 2
Coupling between lines: Vabre modelVoltage in the real space: real voltagesV1 A p e pxVL V2 Vc Vd A e pxVLB p e BepxVLpxVLC p e Ce pxVd Dep pxVd D p epxVdxVdCase of a semi infinite line: reverse voltage is equal to zeroi1e(t)V1 x , p A p eV1i2zV2 px c C p e pV1 o, p A Cx d A C V2 o, z I 2 o, p A C z zc zd e p E p A p a E p C p C E p x xv 2 x, t a e t c e t vc vd a z c z z d z z c z d 2z c z dc z d z z c z z c z d 2z c z dV2 o, t a c e t
Coupling between lines: Vabre modelDefinition of a coupling coefficient k 1 k 1xe t v1 x , t v c v d 22vc 1 v 2 v c v d 2 1 k x e t 2vd 1 ka 2zc zdzc zd zc zdzc 3zdzc zd2 zc zdzc zd3zc zdVabre weak coupling approximationM 1Lzc L MLML 1 # RcccLcM1 L MLLzd c 2 c 1 2 cL# Rccz z c z d k a c z z c z d 2z c z d a c 1 1 kb 2 1c c 11# L M c L c d 11# L M c 2 L c(4)(3)(2)(1)zdzc zdzc
Coupling between lines: Vabre modelEquations in the case of weak coupling: i1 v 1 x L t i v 1 c 1 t x i1 i 2 v 2 x M t L t i v v 2 1 c 2 t t xSecond order equations in the case of weak coupling: ² v1 L c p² v1 0 x ² ²v 2 L c p² v 2 M c L p² v 2 x ²1L c ² v 1 p² v1 0 x² ² 2 ² v 2 p v p² K 1 v1 x ² v 2 v ²K M c L c
Coupling between lines: Vabre modelSolution of the equations:v 1 AeI1 px Bep k 1 x p A e p E k 1 x p B e p v 2 D 2 2 xx 1 v1 1 A e Lp x L x p 1 v 2 I2 M p I1 Lp x Bexp xDe pk1 x e 1 p eI2 Lp xxp k 1 xk 1 p p D p² A A e 2 ²2 v 1 , p I1 , p xv Eex p k 1 x p² B k 1 1 p B MP p E 2 ²2 Lpx k2 x epx xp p x Ae Be
Coupling between lines: Vabre modelLigne 1v 1 p U p e t Y t U p Rc (t) px xxp pk 1 xv 2 D p U p e E e 2 xxp 1 p k 1k 1 x I2 U p p U p E p e e D R c 22 Ligne 2RcRc2 xx p x p pk 1 x v k 1 U p e v e p U p e 242 2 xx p x p p k 1 x1 k 1 I 2 U p e e p U p e R L 42 v
Coupling between lines: Vabre model3 contributions: k 1 t 4 k 1 t 4Direct couplingCoupling after a delayp 2p k 1 n v 2 o, p Û 1 e n p 2p k 1 I 2 o, p Û 1 e n n k - 1 x d 2 dt x décalé de k - 1 x A d Courant : - 2 R c dt Tension induite : - 2 x
Coupling between lines: Vabre modele1 t V1 o, p U p S1 t V1 , p U p e p Near end CrosstalkFar end Crosstalke 2 t V2 o, p S2 t V2 , p e1 t U p Y t S1 t U t Y t e1 t e 2 t k 1 e t e t 2 11S 2 t n k 1 du L d k 1 U p U p e 2 p nsi o 0 k 1 p U p e p 2
Coupling between lines: Vabre model Wave 1 : Coupling at the input of the line: blue line Wave 2 : Coupling at the output of the line: red line Wave 3: Coupling all along the line : black line ( K 1) 4 ( K 1) L2 m ( K 1)4
Coupling between lines: Vabre modelE2RcS2e2S2 k 1U4 tme2RLtm (k - 1) U4 tm2 2 t tmS2si t m (si t m , l'amplitude de e 2est multipliée par 2 )tm
Applied field on a line in reception modeIn this sections, we consider: An infinite line constituted by an infinite wire parallel to a ground planeL I V Ea t x V IC 0 t xEiE a ( z ) E i ( z, h) E i ( z, h)e 2 jk0hIf:h In the time domain:Moreover: V 0 x2 jh E ( z ) E ( z , h)vahi2h E iE ( z) ( z , h)v taThen: I VL Ea t x I 2h E iL tv tI 2h iEZcki
Line in reception modezz dzdV i ( z )ZCZCE a ( z ) E i ( z , h) E i ( z , h)e 2 jk0 hdV i ( z )dI ( z ) 2ZCdV ( z ) E ( z )dziLV (0) Z c dI ( z )ei0LV ( L) Z c dI ( z )ei0 jk0 zL1 E a ( z )e jk0 z dz20 jk0 ( L z )aL1 E a ( z )e jk0 ( L z ) dz20ZsZC2V i (0)Computation of the current along the line: I ( z, p) A( p)e jkx B( p)e jkxZC2 V i ( L) limit conditionsZL
Ligne in reception mode: case of a coaxial lineI ext ( z )Z tr ( f )Vt ( z , f ) Z tr ( z , f ) I ext ( z , f )IdzInternal Voltages Sources the problem is the same aspreviously : integration of the sources and calculation oftheir contribution at the extremites- calculation of the internal currentZsZC2V i (0)ZC2 V i ( L)ZL
Line in reception mode: case of a coaxial line2h E iE (t ) (t )c t2hE (t ) E (t ) E (t )caApplied field on the wire:iV a ( z, t )dI ( z, t ) 2 ZcCurrent elements at the z location :a'aaavec: V ( z, t ) E ( z, t ) zLE i ( z ) jk0 zI (0) e dz2ZC0LzI (0, t ) dI ( z, t )c0iiCurrents at theextremities(L z)I ( L, t ) dI ( z , t )c0LiExternal current along the cable:Internal localvoltage sources:I ( z ) Ae ik0 z Beik0 zv i ( z ) ZT I ( z )LE i ( z ) jk0 ( L z )I ( L) edz2ZC0i
L 400 m 1,33 Ps 10 V 30 V Vtotal 0 Vtotal 30 V 30 V 40 V 10 V z L z L 10 V - 10 V z 0 . Formulation of the direct and forward waves versus parameters Coupled voltage at the input of the line: . Lp I Mp I x v @ 1 @ 2 2 1 2 McL p² V x V J w w 2 @ 1 @ 2 2 LcM p² V x V J w w
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Anatomie et physiologie humaines E. Marieb, 2005 Cheminement de l’air VAS VAI Voies extrathoraciques Voies intrathoraciques 5 . J. West, L’essentiel sur la physiologie respiratoire, ed Maloine, 2003 VAI arbre bronchique 6 . Terminaison de l’arbre bronchique : les alvéoles 7 .
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ASTM C 1702 external mixing Sample 1 Sample 2 Not tested Cement, g 9.81 3.38 Water, g 4.90 1.69 Sand reference, g 37.37 12.61 Test duration, h 168 168 3. Results and Discussion 3.1 Signal to noise Figure 1 shows the heat flow measured from the sample cell charged with sand that displayed the highest overall heat flow. This was taken as a measure of noise for the purpose of this study. Figure 1 .
